Related papers: Truncation error estimates of approximate operator…
Model reduction is a powerful tool in dealing with numerical simulation of large scale dynamic systems for studying complex physical systems. Two major types of model reduction methods for linear time-invariant dynamic systems are Krylov…
This paper considers several approximate operators used in a particle method based on a Voronoi diagram. We introduce and study our approximate operators on gradient and Laplace operators. We derive error estimates for these approximate…
We present a strategy for estimating the error of truncated functional flow equations. While the basic functional renormalization group equation is exact, approximated solutions by means of truncations do not only depend on the choice of…
The truncation and approximation errors for the set of numerical solutions computed by methods based on the algorithms of different structure are calculated and analyzed for the case of the two-dimensional steady inviscid compressible flow.…
The leading asymptotics of the truncation error for Gauss's continued fraction is determined exactly. Not only for this purpose but also for wider applicability elsewhere the discrete analogue of Laplace's method for hypergeometric series…
This work is an attempt to develop an approximate scheme for estimating the volume-based truncation errors in the finite volume analysis of laminar flows. The volume-based truncation error is the net flow error across the faces of a control…
To increase the reliability of simulations by particle methods for incompressible viscous flow problems, convergence studies and improvements of accuracy are considered for a fully explicit particle method for incompressible Navier--Stokes…
We deduce a procedure to apply balanced truncation to parameter-dependent differential-algebraic systems. For that we solve multiple projected Lyapunov equations for different parameter values to compute the Gramians that are required for…
Efficient high order numerical methods for evolving the solution of an ordinary differential equation are widely used. The popular Runge--Kutta methods, linear multi-step methods, and more broadly general linear methods, all have a global…
Balanced truncation, a technique from robust control theory, is a systematic method for producing simple approximate models of complex linear systems. This technique may have significant applications in physics, particularly in the study of…
Partial differential equations (PDEs) with uncertain or random inputs have been considered in many studies of uncertainty quantification. In forward uncertainty quantification, one is interested in analyzing the stochastic response of the…
The article starts with generalizations of some classical results and new truncation error upper bounds in the sampling theorem for bandlimited stochastic processes. Then, it investigates $L_p([0,T])$ and uniform approximations of…
For a sample of Exponentially distributed durations we aim at point estimation and a confidence interval for its parameter. A duration is only observed if it has ended within a certain time interval, determined by a Uniform distribution.…
This paper introduces a novel error estimator for the Proper Generalized Decomposition (PGD) approximation of parametrized equations. The estimator is intrinsically random: It builds on concentration inequalities of Gaussian maps and an…
This paper introduces a new algorithm for numerically computing equilibrium (i.e. stationary) distributions for Markov chains and Markov jump processes with either a very large finite state space or a countably infinite state space. The…
We study gradient-based regularization methods for neural networks. We mainly focus on two regularization methods: the total variation and the Tikhonov regularization. Applying these methods is equivalent to using neural networks to solve…
We propose a method for eliminating the truncation error associated with any subspace diagonalization calculation. The new method, called stochastic error correction, uses Monte Carlo sampling to compute the contribution of the remaining…
When using a finite difference method to solve an initial--boundary--value problem, the truncation error is often of lower order at a few grid points near boundaries than in the interior. Normal mode analysis is a powerful tool to analyze…
Truncating the Fourier transform averaged by means of a generalized Hausdorff operator, we approximate the adjoint to that Hausdorff operator of the given function. We find the formulas for the rate of approximation in various metrics in…
A generalization of Gy's theory for the variance of the fundamental sampling error is reviewed. Practical situations where the generalized model potentially leads to more accurate variance estimates are identified as: clustering of…